I'm wondering if anyone can help, I'm stuck with the following logarithmic equation:

x^3*ln(x)-4x*ln(x)=0

I can easily see why x=1 is a solution (ln(1)=0).Is this the correct procedure for finding the other solutions:

=(x^3-4x)*ln(x)

=x(x^2-4)*ln(x)

=x((x+2)(x-2))*ln(x)

x= -2 or +2

The mark scheme for the past paper says the 2 answers are 1 and -2, but I can't see why 2 isn't a valid solution also? Also, is x=0 not a solution because ln(0) is not defined?